Find a quadratic function with a root at X 5i that also includes the point (2, 14).

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: 1. Find a real root of the equation x³ – 18 = 0, correct to three decimal places by using Bisection…

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: f(x) Vx+1

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Q: Determine the root of the equation x3 – e–x  + 4 by two open methods and round-off your answers to 3…

A: The given equation is: fx=x3-e-x+4 Two open methods are: Newton's method Secant method

Q: 2- Find the approximate roots of the following equation f(x)= 4x – x² -2 = 0 on [0,1], by using…

A: According to the given information it is required to find the approximated roots of the equation…

Q: Use the derivative to find the vertex of parabola. y = -2x2 + 12x - 5

A: Given equation of parabola is y=-2x2+12x-5. To find the vertex using derivative. Solution: We know…

Q: Aregular octagon

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Q: Find the point on the curve y = sqrt x that is closest to thepoint (3,0)

A: Given curve y=x Let A(x,y)  be a point on the curve and let B(3, 0) So distance between A and B is…

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: ved by "the quadratic formula". Be sure to show your work accordingly.

A: We have to choose the correct answer from the given options

Q: Determine the root of the equation x³ + x² = 1 in the interval [0, 1] by using bisection method.

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Q: Find the explicit solution of the separable equation

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

Q: Find the equations of the tangent lines to the parabola y = -x² + 5x – 6 at its points of…

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Q: Find the smallest positive root by using fixed- point method f (x) = In(3x)– x² +2 %3D with three…

A: Given: fx=ln3x-x2+2. We have to find the smallest positive root by using fixed-point method with…

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

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Q: Find an equation of the tangent line to the parabola at the given point. y = –4x2,  (9, –324)

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Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: Use the derivative to find the vertex of each parabola y = ax2 + bx + c

A: Given the function y = ax2 + bx + c We need  to use the derivative to find the vertex of  parabola.

Q: use Newton-Raphson method to obtain a root of equation x'-5x+3=0

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Q: I Pind the root of the function byusing Newton- Raphson method) with Xo1,where fcx> = x²_5x +6

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find an equation of the tangent line to the parabola y=x2  -8x+9 at the point (3, -6)

A: Given :          y= x2-8x+9

Q: use graphs to find approximate solutions ex = 4

A: we have to use the graph to find the approximate solution of ex=4.

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: Find the equation of the line tangent to the graph of f(x) = 7x³ + 8x² – 2x – 6 at x

A: We need to find the equation of the tangent to the function f(x) = 7x3+8x2-2x-6 at x=—2 We know that…

Q: Find the equation of the tangent line to f(x) = 4x² -5x+2 at (-1,11).

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Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: Find the smallest positive root by using fixed-point method f(x) = In(3x)– x² +2 with three…

A: we have f(x)=ln(3x)-x2+2=0 x2=ln(3x)+2x=ln(3x)+2using fixed point iterationxn+1=ln(3xn)+2take…

Q: Use 4-segment the trapezoidal rule to numerically integrate f(x) = f(x)=∛(44x-4) from a = 44 to b…

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Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent…

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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Q: Find a cubic function  y = ax3 + bx2 + cx + d  whose graph has horizontal tangents at the points…

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Q: Find an interval of length 1/4in [1, 2] containing a root of the equation x^7 + 3x − 10 = 0.

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: Find the quadratic approximation to ƒ(x) = 1/(1 - x) atx = 0.

A: Given,  f(x) = 1/(1 - x) at x = 0

Q: A quadratic equation x--4x+43D0 is defined with an initial guess of 10 and 20. Find the approximated…

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Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find a root of an equation f(x) = x^4-2 using Halley's method.

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Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

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Q: Approximate the root of g(x) = 2 + x – eª between 1 and 2 to within 0.05 of the exact value using…

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Q: Find the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function:

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.